Covid: Pizza worker's 'lie' forced South Australia lockdown

South Australia decided to enter a state-wide lockdown after learning a man with Covid-19 had lied about his link to a pizza shop, police say.

The strict six-day lockdown began on Wednesday after the state detected 36 infections, including its first locally acquired cases since April.

But the order would have been avoided if a man had told health officials he had worked "several" shifts at a pizza shop, authorities said.

He had said he was a customer there.

"To say I am fuming is an understatement," state Premier Steven Marshall told reporters on Friday.

Australia has relied on lockdowns, widespread testing and aggressive contact tracing to push daily infections close to zero.